What is the best adhesive/method to use when attaching unfinished wood to a piece of varnished wood?

I want to glue accent pieces of 1/8” thick cherry wood (small detail type pieces) to the surface of already varnished pine. I am concerned that any adhesive I use will damage the varnished surface. I’m hoping someone can recommend an adhesive or method that will allow me to easily do this. I would prefer to avoid scraping off the existing vanish if possible.